X2-(x+4)2=4

Solution for X2-(x+4)2=4 equation:

X2-(X+4)2=4

We move all terms to the left:

X2-(X+4)2-(4)=0

We add all the numbers together, and all the variables

X^2-(X+4)2-4=0

We multiply parentheses

X^2-2X-8-4=0

We add all the numbers together, and all the variables

X^2-2X-12=0

a = 1; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·1·(-12)
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*1}=\frac{2-2\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*1}=\frac{2+2\sqrt{13}}{2}
$